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Anti-gravity refers to the state in which an object defies the laws of gravity.

The cloud city Stratos was built, by the Ardanans, above the surface of the planet Ardana, centuries prior to 2269. The city was described by Spock as "the finest example of sustained anti-gravity elevation [he had] ever seen." (TOS: "The Cloud Minders")

During the 23rd and 24th centuries, the Federation employed anti-gravs and later anti-grav sleds to assist in the moving of large or bulky items. (TOS: "The Changeling"; TNG: "Hollow Pursuits", et al.)

At the same time it was not uncommon to see anti-gravity wheelchairs in use by disabled persons. (TOS: "The Menagerie, Part I"; TNG: "Too Short a Season", et al.) Jadzia Dax, via the Dax symbiont, had been familiar with this type of technology as early as the late 22nd century. (DS9: "Melora")
Anti-gravity is the idea of creating a place or object that is free from the force of gravity. It does not refer to the lack of weight under gravity experienced in free fall or orbit, or to balancing the force of gravity with some other force, such as electromagnetism or aerodynamic lift. Anti-gravity is a recurring concept in science fiction, particularly in the context of spacecraft propulsion. An early example is the gravity blocking substance "Cavorite" in H. G. Wells' The First Men in the Moon.

In Newton's law of universal gravitation, gravity was an external force transmitted by unknown means. In the 20th century, Newton's model was replaced by general relativity where gravity is not a force but the result of the geometry of spacetime. Under general relativity, anti-gravity is impossible except under contrived circumstances.[1][2][3] Quantum physicists have postulated the existence of gravitons, a set of massless elementary particles that transmit the force, and the possibility of creating or destroying these is unclear.

"Anti-gravity" is often used colloquially to refer to devices that look as if they reverse gravity even though they operate through other means, such as lifters, which fly in the air by using electromagnetic fields.[4][5]